Level 3 Differentiation Walkthrough

2025 NCEA Level 3 Differentiation Question 1(c)

2025 Paper

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Question

\[ \text{What is the gradient of the normal to the curve } y=\sin^3x\cos x \text{ when } x=\frac{\pi}{4}\text{?} \]

You must use calculus and show any derivatives that you need to find when solving this problem.

First walkthrough idea

Hint to try first

This is a product of \(\sin^3x\) and \(\cos x\), so start with the product rule.

Step 1

Identify the rule

The function is a product of \(\sin^3x\) and \(\cos x\).

Show the first step’s working

The function is a product of \(\sin^3x\) and \(\cos x\).

Key result

Product rule

Walkthrough overview

What this question practises

This 2025 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Product rule and the gradient of a normal.

This is Question 1(c) from the 2025 NCEA Level 3 Differentiation paper for AS91578 — Apply differentiation methods in solving problems. Use the guided hints to practise the method before revealing the full working.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91578.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise product rule and the gradient of a normal. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Differentiate both factors in turn and keep both product-rule terms.

Continue practising

← Question 1(b) Question 1(d) →